warm marlin
Imagine a slot machine that costs 10 $ for every spin.
There are 2 possible outcomes. Either you get 100 $, or you get nothing.
The chance of getting 100 $ is dependent on a pity system.
The pity system gives 293 Pity Score every time you dont spin 100 $. If your Pity Score is >=5000, you are guaranteed to get 100$. After doing so, 5000 pity score will be subtracted from the current Pity Score.
The dependency is as such:
Chance of getting 100 $ = (ln(Pity Score + 4000))/(100)
What is the expected return for every spin?
My approach. I dont intuitively see a solution .-.
First, I've tried to figure out how many losses are required for the Pity Score to get back to 0 again. (LCM of 293 and 5000 is 1465000).
This is way too many calculations to map out.
Next, I've tried to derive a formula for getting 100 $, but incorporating the pity score. This I have done successfully.
But im not sure if this is the right approach, since i would need to figure out excactly the association between Pity Score and Number of spins, which i dont think there is a straight forward one?
frozen fossil